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\begin{equation*}2 \pi [ \int_0^{9 a^2} 9 a^2 \sqrt{t} \ dt - \int_0^{9 a^2} t \sqrt{t} \ dt] = 2 \pi [9 a^2 \frac{2}{3} t^{ \frac{3}{2} } - \frac{2}{5} t^{ \frac{5}{2}} ]_0^{9 a^2} = 2 \cdot 27 \pi a^5 ( 6 - \frac{2}{5} ) = 54 \pi \frac{28}{5} a^5 = \frac{1512 \pi}{5} a^5\end{equation*}
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